Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points

作者：Gonchenko Sergey V^*; Ovsyannikov Ivan I; Tatjer Joan C

来源：Regular & Chaotic Dynamics, 2014, 19(4): 495-505.

DOI：10.1134/S1560354714040054

• Homoclinic tangency
• rescaling
• 3D Henon map
• bifurcation
• Lorenz-like attractor

It was established in [1] that bifurcations of three-dimensional diffeomorphisms with a homoclinic tangency to a saddle-focus fixed point with the Jacobian equal to 1 can lead to Lorenz-like strange attractors. In the present paper we prove an analogous result for three-dimensional diffeomorphisms with a homoclinic tangency to a saddle fixed point with the Jacobian equal to 1, provided the quadratic homoclinic tangency under consideration is nonsimple.

• 出版日期2014-7